If the difference of the two numbers consists of the same four digits as chosen originally, can you find the four digits?

Say, you have 4 digits, namely: a1, a2, a3, and a4, and that: a1 > a2 > a3 > a4.
To compare 2 4-digit numbers, say abcd, adn efgh, one must first compare the thousands right? If a > e, then abcd > efgh.
If a = e, we continue to compare the hundreds, then... blah blah blah.
Can you get this?
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Now if you want to construct the greatest number from these digits, how can you do that?
Can you go from here? :)

In fact, if you start with any 4-digit number and go through a bunch of iterations (of the Kaprekar Algorithm, each step involving the process described in the OP), you end up with either 0, or the number above.